The over-tilting of type-II Dirac cones has led to various fascinating
quantum phenomena. Here we find two anomalous acoustic plasmons (AAPs) are
dictated by the distinct geometry of two-dimensional (2D) type-II Dirac cones,
far beyond the conventional \text{\ensuremath{\sqrt{q}}} plasmon. One AAP
originates from the strong hybridization of two pockets at one Dirac point,
whereas the other is attributed to the significant enhancement of the band
correlation around the open Fermi surface. Remarkably, the plasmons exhibit
valley-dependent chirality along the tilting direction due to the chiral
electron dispersion. Meanwhile, we discuss the tunability of plasmon dispersion
and lifetime by tuning the gap and dielectric substrate. Our work provides a
promising way to generate the novel plasmons in Dirac materials.Comment: 6 pages, 5 figure